Method of interconnecting nodes and a hyperstar interconnection structure

ABSTRACT

An interconnection structure includes a plurality of nodes and a plurality of information elements. The plurality of nodes are arranged in a regular array having a preselected number N columns and having a preselected number S rows. The preselected number N equals n 2  +n+1, where n is the order of a Perfect Difference Set of the integers {d 0 , d 1 , . . . d n  }. Each node is coupled to nodes in the previous row and the subsequent row according to a diagram of interconnections. In particular, each node (s,j) is coupled to nodes (s-1,  j+d i  !(Mod N)) for i=0, 1, . . . , n; and each node (s,j) is coupled to nodes (s+1, j+d i  !(Mod N)) for i=0, 1, . . . , n. In a method of interconnecting a plurality of nodes, an order n is selected. A Perfect Difference Set comprising the set of {d 0 , d 1 , . . . d n  } is selected. A plurality of nodes are arranged in a regular array having a preselected number N columns and having a preselected number S rows, the preselected number N=n 2  +n+1. Each node (s,j) is coupled to nodes (s-1,  j+d i  !(Mod N)) for i=0, 1, . . . , n. Each node (s,j) is coupled to nodes (s+1,  j+d i  !(Mod N)) for i=0, 1, . . . , n. Information elements are coupled to any of the nodes (s,j), for s=0, 1, . . . , S and j=0, 1, . . . , N-1.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to interconnecting nodes and information elementsin electronic, computer, and communication systems (for example, cellson an integrated circuit, modules in a multiprocessor system, orsubscribers to a telecommunications network). Because of the generalcharacter of the topology that is the foundation of the proposed methodand of the resulting structure, it can be used in hardware as well as insoftware architecture design.

2. Description of Background Art

Optimizing node interconnections is very important for modem electronic,computer, and communication systems. One of the most effective andgeneral architectures of nodes interconnections is based on a full graphdiagram in which each node is connected to every other node. Astraightforward implementation of this architecture, however, cannot berealized practically in devices because of the very large number ofinterconnecting lines between nodes.

Numerous attempts to solve both this problem and the problems of thenumber and the complexity of the switching elements, delay time, etc.were not successful. For example, the well known hypercube architecturediminishes the number of interconnecting lines, but increases the delaytime of information exchanges.

The hypercube architecture has many other disadvantages. Particularly,k-dimensional hypercubes have N=2^(k) vertices, so these structures arerestricted to having exactly 2^(k) nodes. Because structure sizes mustbe a power of 2, there are large gaps in the sizes of systems that canbe built with the hypercubes. This severely restricts the number ofpossible nodes.

A hypercube architecture has a delay time approximately equal to 2 logN, and has a "skew", i.e., different delay times for differentinterconnecting nodes. This creates additional difficulties when usinghypercube structures in system designs.

Similar problems are characteristic of other known methods ofinterconnection and corresponding types of architectures (bus, ring,etc.). Detailed descriptions of the interconnection structures mentionedabove and their main characteristics can be found in H. Sullivan and T.Bashkov, "A large scale, homogenous, fully distributed parallel machine,1." Proc. 4 Symp. Comp. Arch., 1977, pp. 105-117 and in T. L. Casavant,P. Tvrdik, F. Plasil, Parallel computers: theory and practice, IEEEComputer Society Press, Los Alamitos, Calif., 1995, 422 pp., the subjectmatter of both are incorporated herein by reference. Neither one ofthese architectures, however, can ensure an optimal solution to theinterconnection problems.

Consequently, there is a need to develop an interconnecting method andstructure that lacks the above-described shortcomings of knownarchitectures.

SUMMARY OF THE INVENTION

The present invention provides a method for interconnecting a pluralityof nodes. The plurality of nodes are arranged in a regular array havinga preselected number N columns and having a preselected number S rows.The nodes in one row are interconnected to nodes in the previous row andthe subsequent row using relationships based on hyperspace, Galoisfields, and Perfect Difference Sets. An order n is selected for aPerfect Difference Set, which includes the set of integers {d₀, d₁, . .. , d_(n) }. The preselected number N equals n² +n+1. Each node (s,j) iscoupled to nodes (s-1, j+d_(i) !(Mod N)) for i=0, 1, . . . , n. Eachnode (s,j) is coupled to nodes (s+1, j+d_(i) ! (Mod N)) for i=0, 1, . .. , n. Information elements are coupled to nodes (s, j), for s=0, 1, S,and j=0, 1, . . . , N-1.

The present invention also provides an interconnection structure thatincludes a plurality of connecting lines and a plurality of nodesarranged in a regular array having a preselected number N columns andhaving a preselected number S rows. Each node (s,j) is coupled to nodes(s-1, j+d_(i) !(Mod N)), for i=0, 1, . . . , n, and is coupled to nodes(s+1, (j+d_(i))(Mod N)), for i=0, 1, . . . , n. The integers d_(i) arecomponents of a Perfect Difference Set of order n. The preselectednumber N of columns equals n² +n+1. The interconnection structure alsoincludes a plurality of information elements, each of the plurality ofinformation elements is coupled to any of the nodes (s,j), for s=1, 2, .. . , S and j=0, 1, . . . , N-1. The connecting lines couple nodestogether and couple nodes and information elements.

The nodes may be hierarchical nodes (substructures of different levels)with an order of the node less than or equal to the number of inputs ofthe structure of the higher order.

The interconnection structure may be a bipartite interconnectionstructure that includes a plurality of connecting lines and apreselected number 2N of information elements, and includes a pluralityof nodes arranged in a regular array having the preselected number N ofcolumns and having three rows. Each node (0,j) of the first row iscoupled to one of the plurality of information elements by a connectingline. Each node (1,j) of the second row is coupled to the nodes (j+d_(i) !(Mod N)) of the first and third rows for i=0, 1, . . . , n.Each node (2,j) of the third row is coupled to one of the plurality ofinformation elements by a connecting line. The connecting lines couplenodes together and couple nodes and information elements.

The interconnection structure may be a complete hyperstarinterconnection structure in which the nodes of row 0 and row S (i.e.the first and last rows) are integral and form a bi-directional node.Likewise, the information elements include both transmitters andreceivers and are each coupled to one of the bi-directional nodes.

DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view illustrating an intercormection structurearranged on a cylindrical surface.

FIG. 2 is a block diagram illustrating the interconnection structure ofFIG. 1 in a two-dimensional view.

FIG. 3 is a flowchart illustrating the interconnecting of nodes andinformation elements.

FIG. 4 is a block diagram illustrating a bipartite interconnectionstructure in a two-dimensional view.

FIG. 5 is a block diagram illustrating an interconnection structure of acomplete hyperstar structure.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring to FIG. 1, there is shown a perspective view illustrating aninterconnection system 100 that includes an interconnection structure102 arranged on a cylindrical surface 104. Referring to FIG. 2, there isshown a block diagram illustrating the interconnection structure 102 ina two-dimensional view. The interconnection structure 102 includes aplurality of information elements 106, a plurality of nodes 108, and aplurality of connecting lines 110. For clarity, not all of theinformation elements 106, the nodes 108, and the connecting lines 110are labeled in FIGS. 1-2. Also for clarity, the following symbols areused in the figures: nodes 108 are shown as circles; informationelements 106 are shown as squares; and connecting lines 110 are shown aslines coupling nodes 108 together or as lines coupling nodes 108 andinformation elements 106.

Referring in particular to FIG. 2, the nodes 108 of the interconnectionstructure 102 of FIG. 1 are shown in FIG. 2 in a linear configurationcut along a line 112 (FIG. 1) and repeated, so that all nodes 108 to theleft of a left broken line 200, and to the right of a right broken line202 are the same nodes 108 with corresponding numbers that are betweenthe lines 200 and 202. For clarity, FIG. 2 does not show the informationelements 106.

The nodes 108 are arranged in a regular array of a preselected number Nof columns and a preselected number S of rows. The nodes 108 may be, forexample, switching circuits or interconnection circuits, such ascrossbar switches. The information elements 106 may be, for example,transmitters or receivers or both. The connecting lines 110 may be, forexample, circuit traces on an integrated circuit or communication lines.

The interconnection structure and the method of interconnecting of thepresent invention use hyperspace, Galois fields, and Perfect DifferenceSets (PDS). Perfect Difference Sets were first introduced in J. Singer,"A theorem in finite projective geometry and some applications to numbertheory," Trans. Amer. Math. Soc., v. 43, 1938, pp. 377-385, the subjectmatter of which is incorporated herein by reference, and were laterdeveloped in numerous works on group theory, finite projectivegeometries and number theory, particularly in M. Hall, Jr. The theory ofgroups, 2nd ed., Chelsea Publishing Company, N.Y., 1976, 340 pp., thesubject matter of which is incorporated herein by reference.

A Perfect Difference Set of n-th order is a collection of integers

    {d.sub.0, d.sub.1, d.sub.2, . . . , d.sub.i, . . . , d.sub.n }(1)

having some special properties. This collection of integers iscyclically organized (i.e., d₀ and d_(n) are considered as beingconsecutive):

    . . . d.sub.n, d.sub.0, d.sub.1, . . . d.sub.i, . . . , d.sub.n, d.sub.0, . . .

Operations over the elements of the Perfect Difference Set are performedusing modulo N arithmetic, where the base N of the modulo operator isdetermined by the equation:

    N=n.sup.2 +n+1,                                            (2)

where n is the order of the Perfect Difference Set. Because they arebased on an augmented Galois fields {GF(n) fields}, Perfect DifferenceSets exist for every order n:

    n=p.sup.r,                                                 (3),

where p is a prime number and r is an integer.

The Perfect Difference Set establishes the interconnections in themethod and structure of the present invention, and the structure can beconstructed for every prime power n=p^(r). This provides a largeadvantage over the hypercube architecture, where structures exist onlyfor the powers of 2.

Both of these approaches use hyperspace, but the hyperspace constructionused in the present invention is more flexible than the one used inhypercubes. As a result, a new architecture (which can be calledhyperstar) is revealed, which lacks many of the limitations anddisadvantages of a hypercube architecture.

For example, the values of the order n for which an interconnectionstructure can be constructed in a hyperstar architecture are:

    2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 19, 23, 25, 27, 29, 31, 32, . . .

In contrast, for a hypercube architecture, in the same interval,construction exists only for the values of n:

    2, 4, 8, 16, 32, . . .

Table I shows examples of the Perfect Difference Set for several ordersof sets.

                  TABLE I                                                         ______________________________________                                        n           N         PDS                                                     ______________________________________                                        2            7        {0,1,3}                                                 3           13        {0,1,3,9}                                               3           13        {0,1,4,6}                                               4           21        {0,1,4,14,16}                                           5           31        {0,1,3,8,12,18}                                         5           31        {0,1,4,6,13,21}                                         5           31        {0,1,8,11,13,17}                                        7           57        {0,1,3,13,32,36,43,52}                                  ______________________________________                                    

Methods for constructing Perfect Difference Sets are well known and aredescribed in M. Hall, Jr., "A survey of difference sets," Proc. Amer.Math. Soc., v. 7, 1956, pp. 975-986 and in M. Sverdlik, "Optimaldiscrete signals" (in Russian), Soviet Radio, Moscow, 1975, 200 pp., thesubject matter of both is incorporated herein by reference.

Referring again to FIGS. 1-2, the nodes 108 are coupled to other nodes108 by the connecting lines 110 according to a diagram ofinterconnections (described below), which in turn is based on thePerfect Difference Set (described above). The nodes 108 in each row ofthe array are numbered as nodes 0 through N-1. Each j-th node 108 (forj=0, 1, . . . , N-1) is coupled to groups of (n+1) nodes 108 in thesubsequent row and in the preceding row according to the expression:

     j+d.sub.i !(mod N)                                        (3)

for i=0, 1, . . . , n, and where d_(i) are elements of a PerfectDifference Set of order n.

The diagram of interconnections of the nodes 108 is a matrix ofdimensions (n+1)×N. The elements of the matrix are calculated usingequation (3) and j is the number of the node 108 in the regular arrayand i is the number of the component of the Perfect Difference Set.Tables II through V are examples of the diagrams of interconnections.For example, in the interconnection structure of Table 11, for each row,the fifth node 108 (j=5) is coupled to nodes 108 for j=5,j=6 and j=1, inthe subsequent and preceding rows (as indicated in the row of Table IIthat is in bold numbers).

Table II shows the interconnections for an n=2, N=7, PDS={0, 1, 3}structure.

                  TABLE II                                                        ______________________________________                                        j          i        1         2       3                                       ______________________________________                                        0                   0         1       3                                       1                   1         2       4                                       2                   2         3       5                                       3                   3         4       6                                       4                   4         5       0                                       5                   5         6       1                                       6                   6         0       2                                       ______________________________________                                    

Table III shows the interconnections for an n=3, N=13, PDS={0, 1, 3, 9}structure.

                  TABLE III                                                       ______________________________________                                        j      i         1      2         3    4                                      ______________________________________                                        0                0      1         3    9                                      1                1      2         4    10                                     2                2      3         5    11                                     3                3      4         6    12                                     4                4      5         7    0                                      5                5      6         8    1                                      6                6      7         9    2                                      7                7      8         10   3                                      8                8      9         11   4                                      9                9      10        12   5                                      10               10     11        0    6                                      11               11     12        1    7                                      12               12     0         2    8                                      ______________________________________                                    

Table IV shows the interconnections for an n=3, N=13, PDS={0, 1, 4, 6}structure.

                  TABLE IV                                                        ______________________________________                                        j      i        1      2        3    4                                        ______________________________________                                        0               0      1        4    6                                        1               1      2        5    7                                        2               2      3        6    8                                        3               3      4        7    9                                        4               4      5        8    10                                       5               5      6        9    11                                       6               6      7        10   12                                       7               7      8        11   0                                        8               8      9        12   1                                        9               9      10       0    2                                        10              10     11       1    3                                        11              11     12       2    4                                        12              12     0        3    5                                        ______________________________________                                    

Table V shows the interconnections for an n=4, N=21, PDS={0, 1, 4, 14,16} structure.

                  TABLE V                                                         ______________________________________                                        j        i    1         2   3       4   5                                     ______________________________________                                         0             0         1   4      14  16                                     1             1         2   5      15  17                                     2             2         3   6      16  18                                     3             3         4   7      17  19                                     4             4         5   8      18  20                                     5             5         6   9      19   0                                     6             6         7  10      20   1                                     7             7         8  11       0   2                                     8             8         9  12       1   3                                     9             9        10  13       2   4                                    10            10        11  14       3   5                                    11            11        12  14       3   5                                    12            12        13  16       5   7                                    13            13        14  17       6   8                                    14            14        15  18       7   9                                    15            15        16  19       8  10                                    16            16        17  20       9  11                                    17            17        18   0      10  12                                    18            18        19   1      11  13                                    19            19        20   2      12  14                                    20            20         0   3      13  15                                    ______________________________________                                    

The interconnection structure includes a plurality of nodes and aplurality of connecting lines 110. The plurality of nodes is arranged ina regular array having a preselected number N columns and having apreselected number S rows. Each node (s,j) is coupled to nodes (s-1,j+d_(i) !(Mod N)) by n+1 connecting lines 110, for i=0, 1, . . . , n,and also is coupled to nodes (s+1, (j+d_(i))(Mod N)) by n+1 connectinglines 110, for i=0, 1, . . . , n. The d_(i) are components of a PerfectDifference Set of order n and the number of preselected number N ofcolumns equals n² +n+1.

As described below, the nodes 108 may be substructures that also aregenerated from the diagram of interconnections or may be simplerinterconnections.

The topology of the interconnection structure 102 does not depend on theconcrete physical nature of the signals (messages) and technical means(connecting lines, switches etc.). It can be applied to the solving ofhardware as well as software organization problems in electronics andcommunication, in transport problems, and so on. In the case ofsoftware, information elements, nodes and connecting lines mayrepresent, for example, objects, entilies, vertices and connections,relationships, and edges.

Referring to FIG. 3, there is shown a flowchart illustrating theinterconnecting of nodes 108 and information elements 106. An order n ofthe interconnection structure is selected (block 302). The order n maybe user selected or selected in a predefined manner. A PerfectDifference Set of order n and comprising the set of integers {d₀, d₁, .. . d_(n) } is selected (block 304). The Perfect Difference Set may beuser selected or selected in a predefined manner. A plurality of nodes108 are arranged in a regular array having a preselected number Ncolumns and having a preselected number S rows (block 306). Thepreselected number N equals n² +n+1. The number N preferably is greaterthan the number of inputs to the structure. The preselected number S isa number that is determined by the required total number of informationelements for a specific application.

Each node 108 is designated in a conventional format by the row s andthe column j as node (s,j). Each node 108 (s,j) is coupled to nodes 108(s-1, j+d_(i) !(Mod N)) for i=0, 1, . . . , n by n+1 connecting lines110. Likewise, each node (s,j) is coupled to nodes 108 (s+1, j+d_(i)!(Mod N)) for i=0, 1, . . . , n by n+1 connecting lines 110. The nodes108 and the connecting lines 110 form the interconnection structure 102.

Information elements 106 are coupled to corresponding nodes (s,j), fors=0, 1, . . . , S, and j=0, 1, . . . , N-1 (block 308). Of course somenodes 108 may not be coupled to information elements 106.

Referring to FIG. 4, there is shown a block diagram illustrating abipartite interconnection structure 400 in a two-dimensional view. Thebipartite structure 400 is a particular case of the interconnectionstructure of FIGS. 1-2. Specifically, the bipartite graph (also known asK_(N),N graph) has equal numbers of vertices in the first and last rows.The bipartite interconnection structure 400 ensures that informationexchanges between each of the N information elements 106 of the upperrow and each of the N information elements 106 of the lower row, andvice versa.

Topologically these information elements 106 and nodes 108 are placed onthe cylindrical surface 104 (FIG. 1). In a manner similar to that ofFIG. 2, the bipartite interconnection structure 400 is shown in FIG. 4in a linear configuration and repeated, so that all information elements106 and nodes 108 to the left of a left broken line 402, and to theright of a right broken line 404 are the same information elements 106and nodes 108 with corresponding numbers that are between the lines 402and 404.

The bipartite interconnection structure 400 includes a preselectednumber N of information elements 106, a plurality of nodes 108, and aplurality of connecting lines 110. The plurality of nodes 108 arearranged in a regular array having the preselected number N of columnsand having three rows. Each node (1,j) of the second row is coupled tothe nodes 108 ( j+d_(i) !(Mod N)) of the first and third (outer) rowsfor i=0, 1, . . . , n by n+1 connecting lines 110. As above, the numbersd_(i) are components of a Perfect Difference Set of order n. Thepreselected number N of columns equals n² +n+1.

Each of the plurality of information elements 106 is coupled to acorresponding node (0,j), for j=0, 1, . . . , N-1. Of course some nodes108 may not have information elements 106 coupled to them. The outernodes 108 are coupled to respective ones of the information elements106. In particular, each node (0,j) of row 0 is coupled to one of theplurality of information elements 106 by the connecting lines 110.Likewise, each node (2,j) of row 2 is coupled to information elements jby the connecting lines 110. The nodes 108 in row 0 and row 2 may beintegral with a bi-directional node 108. Likewise, the informationelements 106 coupled to the row 0 of the nodes 108 and the informationelements 106 coupled to the row 2 of the nodes 108 may be integral witha transmiting and receiving information element 106.

Referring to FIG. 5, there is shown a block diagram illustrating acomplete hyperstar interconnection structure 500. To generate thecomplete interconnection structure 500, the upper information elements106 are considered to be transmiters of information, and lowerinformation elements 106 are considered to be receivers. The completehyperstar structure is realized by wrapping-around the interconnectionstructure of FIG. 4 to combine the transmitting information elements 106and the receiving information elements 106 into a transmitter-receiverinformation element and to combine nodes 108 into bi-directional nodes108. The resulting configuration is a torus. The interconnectionstructure 500 shows three rows of nodes 108 with the nodes of rows 0 and2 combined into a bi-directional node 108.

The complete interconnection structure 500 includes a preselected numberN of information elements 106, a plurality of nodes 108, and a pluralityof connecting lines 110. The plurality of nodes is arranged in a regulararray having the preselected number N of columns and having to rows.Each node (0,j) of the first row is coupled to an information element jby bi-directional connecting lines 110, for j=0, 1, . . . ,n. Each node(0,j) is also coupled to the nodes 108 (1,j) of the second row (j+di!(Mod N)) by n+1 bi-directional connecting lines 110, for i=0, 1 , .. . , n. As before, the integers d_(i) are components of a PerfectDifference Set of order n. The preselected number N of columns equals n²+n+1.

For the known fully connected network, the total number of links isproportional to N×(N-1). In contrast, in the present invention, thenumber of links is proportional to only N×(n+1). Taking into accountthat in the interconnection of the present invention, N=n² +n+1, andthus, for large values of N, (which are of most interest), a coefficientof the diminishing of number of interconnections C_(c) is proportionalto N^(1/2). Table VI shows proportional values of interconnecting linksfor these two cases for various values of n and N.

                  TABLE VI                                                        ______________________________________                                        n        N     Full graph   New Structure                                                                          C.sub.c                                  ______________________________________                                        2         7     21           21      1                                        3        13     78           52      1.5                                      4        21     231         105      2.2                                      5        31     465         186      2.5                                      7        57    1596         465      3.5                                      8        73    2628         657      4.0                                      ______________________________________                                    

Improvement of the characteristic is considerable even for relativelysmall number of nodes 108, and increases dramatically for large numbers.For example, a system with 9507 nodes 108 has C_(c) ≅50.

Maximal improvement of characteristics is achieved when the real numberof nodes N' is equal to N; the number N itself does not take all valuesfrom the natural row (see Table VII). However, the leaps of N are notlarge (and significantly less than in the case of the hypercubearchitecture). Excessive connections in the case N'<N can be eithereliminated or used to increase system reliability.

                  TABLE VII                                                       ______________________________________                                        n        N                Δ(N.sub.i /N.sub.i-1)%                        ______________________________________                                         2         7              --                                                   3        13              86                                                   4        21              60                                                   5        31              48                                                   7        57              83                                                   8        73              28                                                   9        91              25                                                  11        133             46                                                  13        183             36                                                  16        273             49                                                  17        307             12                                                  19        381             13                                                  23        553             45                                                  25        651             18                                                  27        757             16                                                  29        871             15                                                  31        993             14                                                  32       1057              7                                                  37       1407             33                                                  41       1723             23                                                  43       1893             10                                                  47       2257             19                                                  49       2451              9                                                  53       2863             16                                                  59       3541             19                                                  61       3783              7                                                  64       4161             10                                                  67       4557             10                                                  71       5113             11                                                  73       5403              7                                                  79       6321             17                                                  81       6643              8                                                  83       6973              5                                                  97       9507             19                                                  ______________________________________                                    

As shown in Table VII, for large N, the leaps between values of N do notexceed 20%. In contrast, for a hypercube architecture, the leap alwaysis equal to 100%. Another, and much more important difference betweenthe structures of the present invention and the hypercube architectureis that, in the former, the connection between any nodes 108 in adjacentrows is always achieved in one hop, and the "skew" is equal to zero. Asa result, the exchange between information elements 106 is performedwith minimal possible delay, and all delays are equal. It makesinterconnection structure of the present invention very convenient,particularly for the use in integrated circuits and multiprocessorcomputer systems design.

The total complexity of the interconnection structure depends on thecomplexity of the nodes 108 that form the whole array. These nodes 108in the general case have number of inputs proportional to (n+1) whichare used for interconnection of nodes 108 with one another, as well asadditional inputs for the information elements 106(transmitters-receivers of information).

Information elements 106 can be connected to any node in the generalarray.

In the most general case, to avoid the effect of blocking (a conflictsituation when several information element use the same interconnectingnode), these nodes 108 must have the ability to interconnectsimultaneously a number of links that is proportional to (n+1). Thisrequires a large number of switches and leads to the seriouscomplication of the structure in general. Fortunately, in practice thenumber of information elements 106 interconnecting through any node issignificantly less and proportional to only m, where:

    m<(n+1)                                                    (4)

Thus, the interconnection structure may include nodes that aresubstructures having the ability to interconnect m of (n+1) inputs,where m<(n+1).

This fact follows from the general considerations based on the theory ofprobabilities and is confirmed by computer simulations.

An example is given in the Table VII for n=32, N=1057 for an experimentwith a total number of trials of

                  TABLE VII                                                       ______________________________________                                        Number of paths                                                                            Number of trials with                                            through node this number of paths                                                                        Fraction of trials                                 ______________________________________                                        0            324           32%                                                1            414           41%                                                2            198           20%                                                3             54            5%                                                4             10            1%                                                5-33          0             0%                                                ______________________________________                                    

As a result, in practical applications instead of a complex system thatis able to fully interconnect up to 33 inputs/outputs, we can use adramatically simpler node that is able to interconnect only 4 to 5 ofthe total number of links, thereby requiring far fewer switchingelements.

The interconnection structure may comprise a set of hierarchical nodes108 with the hierarchical nodes 108 further comprising hierarchicalnodes 108 of different levels with the orders and numbers of inputsaccording to the sequence:

     n.sub.1, N.sub.1 ; n.sub.2,N.sub.2 ; . . . ; n.sub.q,N.sub.q ; . . . !(5)

where n_(q+1) ≦N_(q).

Such an interconnection structure includes a plurality of hierarchicalnodes 108 (sub-structures) arranged in a regular array having apreselected number N_(a) columns and having a preselected number S rows.Each node (s,j) is coupled to nodes 108 (s-1, j+d_(i) !(Mod N_(a))) byn_(a) +1 connecting lines 110, for i=0, 1, . . . , n_(a), and also iscoupled to nodes 108 (s+1, (j+d_(i))(Mod N_(a))) by n_(a) +1 connectinglines 110, for i=0, 1, . . . , n_(a). As before, d_(i) are components ofa Perfect Difference Set of order n_(a). The preselected number N_(a) ofcolumns equals n_(a) ² +n_(a) +1.

Any of the plurality of hierarchical nodes 108 further includes aplurality of hierarchical nodes 108 arranged in a regular array having apreselected number N_(b) columns and having a preselected number S'rows. Each node (s,j) is coupled to nodes (s'-1, j+d_(i) !(Mod N_(b)))by n_(b) +1 connecting lines 110, for i=0, 1, . . . , n_(b), and iscoupled to node (s'+1, (j+d_(i))(Mod N_(b))) by n_(b) +1 connectinglines 110, for i=0, 1, . . . , n_(b). Again, d_(i) are components of aPerfect Difference Set of order n_(b) and the preselected number N_(b)of columns equals n_(b) ² +n_(b) +1. The order n_(b) of the lower levelof the hierarchical set and the preselected number N_(b) of columns areselected from the sequence defined above in equation (5).

Generally, the type of the intermediate substructures and the number ofhierarchical levels can vary depending on the total number of nodes 108and requirements to the principles of the exchange information betweenthem. Sometimes it is possible to use a simple substructure, up to thedirect connection or simplest commutator-multiplexer. These structurescan be considered a particular case of the general solution of theinterconnection problem.

The hyperstar interconnection structure combines most of the advantagesof well known architectures, such as the fully connected system and thehypercube architecture, and at the same time is free of most of theirshortcomings. It is unique in combination of high speed of informationexchange, low number of interconnecting links and a reasonable number ofswitching elements. This structure is a real landmark in the theory andpractice of node interconnections.

I claim:
 1. A method of interconnecting a plurality of nodes, the methodcomprising the steps of:selecting an order n; selecting a PerfectDifference Set comprising the set of {d₀,d₁, . . . d_(n) }; arranging aplurality of nodes in a regular array having a preselected number Ncolumns and having a preselected number S rows, the preselected numberN=n² +n+1; coupling each node (s,j) to nodes (s-1, j+d_(i) !(Mod N)) fori=0, 1, . . . , n; and coupling each node (s,j) to nodes (s+1, j+d_(i)!(Mod N)) for i=0, 1, . . . , n.
 2. The method of claim 1 furthercomprising the step of:coupling information elements to nodes (s,j), fors=0, 1, . . . , S, and j=0, 1, . . . , N-1.
 3. An interconnectionstructure comprising:a plurality of nodes arranged in a regular arrayhaving a preselected number N columns and having a preselected number Srows, each node (s,j) being coupled to nodes (s-1, j+d_(i) !(Mod N)),for i=0, 1, . . . , n, and being coupled to nodes (s+1, (j+d_(i))(ModN)), for i=0, 1, . . . , n, where d_(i) are components of a PerfectDifference Set of order n and the preselected number N of columns equalsn² +n+1.
 4. The interconnection structure of claim 3 further comprisinga plurality of connecting lines providing said coupling between nodes.5. The interconnection structure of claim 3 further comprising aplurality of information elements, each of the plurality of informationelements being coupled to any of the nodes (s,j), for s=1, 2, . . . , Sand j=0, 1, . . . , N-1.
 6. The interconnection structure of claim 5further comprising a plurality of connecting lines providing saidcoupling between nodes and between nodes and the plurality ofinformation elements.
 7. The interconnection structure of claim 5wherein each information element comprises a transmitter and a receiver.8. The interconnection structure of claim 3 wherein any of the pluralityof nodes comprises a plurality of substructures of order n' and a numberN' of inputs, where N'=n^('2) +n'+1 and n'≦N.
 9. An interconnectionstructure comprising:a plurality of hierarchical nodes arranged in aregular array having a preselected number N_(a) columns and having apreselected number S rows, each node (s,j) being coupled to nodes (s-1,j+d_(i) !(Mod N_(a))), for i=0, 1, . . . , n_(a), and being coupled tonode (s+1, (j+d_(i))(Mod N_(a))), for i=0, 1, . . . , n_(a), where d_(i)are components of a Perfect Difference Set of order n_(a) and thepreselected number N_(a) of columns equals n_(a) ² +n_(a) +1, any of theplurality of hierarchical nodes comprising a plurality of hierarchicalnodes arranged in a regular array having a preselected number N_(b)columns and having a preselected number S' rows, each node (s,j) beingcoupled to node (s'-1, j+d_(i) !(Mod N_(b))), for i=0, 1, . . . , n_(b),and being coupled to node (s'+1,(j+d_(i))(Mod N_(b))), for i=0, 1, . . ., n_(b), where d_(i) are components of a Perfect Difference Set of ordern_(b) and the preselected number N_(b) =n_(b) ² +n_(b) +1, the numbern_(b) ≦N_(a).
 10. A bipartite interconnection structure comprising:apreselected number 2N of information elements; and a plurality of nodesarranged in a regular array having the preselected number N of columnsand having three rows, each node (0,j) of the first row and each node(2,j) of the third row being coupled to one of the plurality ofinformation elements, each node of the second row (1,j) being coupled tothe nodes of the first and second rows ( j+di!(Mod N)) for j=0, . . . ,Nand i=0, 1, . . . ,n, where d_(i) are components of a Perfect DifferenceSet of order n and the preselected number N of columns equals n² +n+1.11. A complete hyperstar interconnection structure comprising:apreselected number N of information elements; and a plurality of nodesarranged in a regular array having the preselected number N of columnsand having two rows, each node (0,j) of the first row being coupled tonodes of the second row (1,(j+d_(i))(Mod N)), for j=0, 1, . . . ,N andi=0, 1, . . . , n, where d_(i) are components of a Perfect DifferenceSet of order n, and the preselected number N of columns equals n² =n+1.12. The interconnection structure of claim 11 wherein for j=0, . . . ,N, node (0,j) and node (1,j) are integral with a bi-directional node j.